Solve 0.2x^2+8x-240=0

$$0.2 { x }^{ 2 } +8x-240=0$$

Solve for x

$$x=-60$$

$$x=20$$

Steps Using the Quadratic Formula

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$0.2x^{2}+8x-240=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.2 for a, 8 for b, and -240 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\times 0.2\left(-240\right)}}{2\times 0.2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\times 0.2\left(-240\right)}}{2\times 0.2}$$

Multiply -4 times 0.2.

$$x=\frac{-8±\sqrt{64-0.8\left(-240\right)}}{2\times 0.2}$$

Multiply -0.8 times -240.

$$x=\frac{-8±\sqrt{64+192}}{2\times 0.2}$$

Add 64 to 192.

$$x=\frac{-8±\sqrt{256}}{2\times 0.2}$$

Take the square root of 256.

$$x=\frac{-8±16}{2\times 0.2}$$

Multiply 2 times 0.2.

$$x=\frac{-8±16}{0.4}$$

Now solve the equation x=\frac{-8±16}{0.4} when ± is plus. Add -8 to 16.

$$x=\frac{8}{0.4}$$

Divide 8 by 0.4 by multiplying 8 by the reciprocal of 0.4.

$$x=20$$

Now solve the equation x=\frac{-8±16}{0.4} when ± is minus. Subtract 16 from -8.

$$x=-\frac{24}{0.4}$$

Divide -24 by 0.4 by multiplying -24 by the reciprocal of 0.4.

$$x=-60$$

The equation is now solved.

$$x=20 x=-60$$

Steps for Completing the Square

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$0.2x^{2}+8x-240=0$$

Add 240 to both sides of the equation.

$$0.2x^{2}+8x-240-\left(-240\right)=-\left(-240\right)$$

Subtracting -240 from itself leaves 0.

$$0.2x^{2}+8x=-\left(-240\right)$$

Subtract -240 from 0.

$$0.2x^{2}+8x=240$$

Multiply both sides by 5.

$$\frac{0.2x^{2}+8x}{0.2}=\frac{240}{0.2}$$

Dividing by 0.2 undoes the multiplication by 0.2.

$$x^{2}+\frac{8}{0.2}x=\frac{240}{0.2}$$

Divide 8 by 0.2 by multiplying 8 by the reciprocal of 0.2.

$$x^{2}+40x=\frac{240}{0.2}$$

Divide 240 by 0.2 by multiplying 240 by the reciprocal of 0.2.

$$x^{2}+40x=1200$$

Divide 40, the coefficient of the x term, by 2 to get 20. Then add the square of 20 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+40x+20^{2}=1200+20^{2}$$

Square 20.

$$x^{2}+40x+400=1200+400$$

Add 1200 to 400.

$$x^{2}+40x+400=1600$$

Factor x^{2}+40x+400. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+20\right)^{2}=1600$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+20\right)^{2}}=\sqrt{1600}$$

Simplify.

$$x+20=40 x+20=-40$$

Subtract 20 from both sides of the equation.

$$x=20 x=-60$$